Tata Institute of Fundamental Research

Heterogeneous arrival streams in a two-queue network

Project Presentation
Speaker: Agniv Bandyopadhyay
Organiser: Sandeep K Juneja
Date: Friday, 23 Dec 2022, 16:00 to 17:00
Venue: A201

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Abstract:  In a concert queuing game, users decide when to arrive at a bottleneck queue of constant capacity that opens at a specific time. Every user wants to simultaneously minimize her waiting time and get served as early as possible. In previous incarnations, this game has been studied over a single queue and over networks with specific topologies such as tandem networks, trellis networks, and general feed-forward networks having multiple layers, with users arriving at one extreme layer and traveling to the other extreme. A unique non-cooperative Nash Equilibrium profile has been identified in the case of the single queue and tandem networks with multiple layers. Whereas for trellis networks and general feed-forward networks, the existence of non-cooperative Nash Equilibrium profiles has been proved. It has also been proven that if there are multiple such equilibriums, they will all have an equal social cost. In this project, we attempt to study the situation where multiple classes of players are traveling through different paths in a queuing network. For simplicity, we consider two groups of players who intend to travel on two distinct paths in a two-queue network. We also assume that all players in a group have identical preferences. In all these instances, we can find a unique non-cooperative Nash Equilibrium profile as long as the two groups have different preferences. Also, in equilibrium, the two groups will choose their order of arrival depending on how their population sizes compare. We also observe that whenever the two groups share one queue in their path, if the queue's capacity is under an identified threshold, the two groups will arrive in that queue in contiguous disjoint intervals. On the other hand, if it is strictly above that threshold, the two groups will arrive together in that queue over some contiguous interval in the equilibrium profile.